On upper bounds for infinite Prandtl number convection with or without rotation

Abstract Bounds for the bulk heat transport in Rayleigh-Benard convection for an infinite Prandtl number fluid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number N u) is bounded in terms of the nondimensional temperature difference across the layer (the Rayleigh number Ra) according to where c < 1 is an absolute constant. This rigorous upper limit is uniform in the rotation rate when a Coriolis force, corresponding to the rotating convection problem, is included